In an article which first appeared in The Times and is now on the BBC's The Editors' blog, Thompson argues: "Whatever the ultimate conclusions of the Leveson inquiry, it is important that the ability of serious investigative journalists to do their work is not blunted or unnecessarily constrained.
"Nor I believe should we automatically assume that newspapers should be held to the same level of regulatory supervision and constraint as the broadcasters. Plurality of regulation is itself an important safeguard of media freedom."
He points out: "The BBC is paid for by the public. Because of that, we would never have paid for the stolen information that helped the Daily Telegraph to uncover the MPs' expenses scandal. The privately owned Telegraph took a different view and was able to publish a series of stories that, taken as a whole, were clearly in the public interest. It is not obvious to me that newspapers that people can choose to buy or ignore - and which, should they break the law, can always be prosecuted after the fact - should be held to the same level of continuous supervision and accountability as broadcasters who reach out into every household in the land."
Thompson also crticises those newspapers that ignored the phone hacking story. "But there are still searching questions for British journalism to answer. Many newspapers with strong investigative teams and many notable journalists with an outstanding record of holding other institutions and walks of life to account showed a marked reluctance to explore the phone-hacking story until events and the public furore made it inevitable. In some cases, they not only refused to investigate the story themselves but heaped opprobrium on those that did. According to Stephen Glover, writing some months ago in the Independent, for example, 'the BBC has conspired with the Guardian to heat up an old story and attack Murdoch'.
"Even in recent days, there's been an attempt in papers that have nothing to do with News International to suggest that our coverage of the story is far more extensive than other news providers and motivated by spite or glee rather than proper news priorities.
"The Daily Mail quoted an Ipsos Mori poll misleadingly this week to suggest that public interest in the story is low. On the contrary, our tracking data suggests it is widespread, with more than 54% of adults claiming to follow the story closely."
Thompson concludes:"I believe that what the public want, what this moment demands, is not another round of self-serving hypocrisy or internecine strife from Britain's journalists, but a serious discussion about the difference between good and bad investigative journalism and a complex but necessary debate about where the boundary of acceptable journalistic practice lies and how it should be enforced."